I've spent all evening working on it, and had to make a trip to Lowe's, but I have installed a new garbage disposal (Waste King L-8000). I was even able to remove an unnecessary piece of pipe and its compression fitting. The new disposal is quieter and twice as strong. And so far there are no leaks, despite the fact that this was my first time using plumber's putty.

I'll feel better after a few days of no leaks, though. Why does water have to ruin everything?